An economics professor uses a virtual classroom session and allows students to take the midterm exam as many times as needed until a passing grade is obtained. Following is a record of the number of students in a class of 20 who took the test each number of times. Students Number of Tests 10 1 7 2 2 3 1 4 a. Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition. (3) b. Find the expected value of the number of tests taken. (2) c. Compute the variance. (2) d. Compute the standard deviation. (2)